Definition for Value SetProbabilityDistributionType

<?xml version="1.0" encoding="UTF-8"?>

<ValueSet xmlns="http://hl7.org/fhir">
  <id value="probability-distribution-type"/> 
  <meta> 
    <lastUpdated value="2022-09-07T10:58:29.429+10:00"/> 
    <profile value="http://hl7.org/fhir/StructureDefinition/shareablevalueset"/> 
  </meta> 
  <text> 
    <status value="extensions"/> 
    <div xmlns="http://www.w3.org/1999/xhtml">
      <ul> 
        <li> Include these codes as defined in 
          <a href="http://terminology.hl7.org/3.1.0/CodeSystem-v3-ProbabilityDistributionType.html">
            <code> http://terminology.hl7.org/CodeSystem/v3-ProbabilityDistributionType</code> 
          </a> 
          <table class="none">
            <tr> 
              <td style="white-space:nowrap">
                <b> Code</b> 
              </td> 
              <td> 
                <b> Display</b> 
              </td> 
              <td> 
                <b> Definition</b> 
              </td> 
            </tr> 
            <tr> 
              <td> 
                <a href="http://terminology.hl7.org/3.1.0/CodeSystem-v3-ProbabilityDistributionType.html#v3-ProbabilityDistri
                butionType-B">B</a> 
              </td> 
              <td> beta</td> 
              <td> The beta-distribution is used for data that is bounded on both sides and might or might
                 not be skewed (e.g., occurs when probabilities are estimated.) Two parameters a and b
                 are available to adjust the curve. The mean m and variance s2 relate as follows: m = a/
                 (a + b) and s2 = ab/((a + b)2 (a + b + 1)).</td> 
            </tr> 
            <tr> 
              <td> 
                <a href="http://terminology.hl7.org/3.1.0/CodeSystem-v3-ProbabilityDistributionType.html#v3-ProbabilityDistri
                butionType-E">E</a> 
              </td> 
              <td> exponential</td> 
              <td> Used for data that describes extinction. The exponential distribution is a special form
                 of g-distribution where a = 1, hence, the relationship to mean m and variance s2 are m
                 = b and s2 = b2.</td> 
            </tr> 
            <tr> 
              <td> 
                <a href="http://terminology.hl7.org/3.1.0/CodeSystem-v3-ProbabilityDistributionType.html#v3-ProbabilityDistri
                butionType-F">F</a> 
              </td> 
              <td> F</td> 
              <td> Used to describe the quotient of two c2 random variables. The F-distribution has two parameters
                 n1 and n2, which are the numbers of degrees of freedom of the numerator and denominator
                 variable respectively. The relationship to mean m and variance s2 are: m = n2 / (n2 -
                 2) and s2 = (2 n2 (n2 + n1 - 2)) / (n1 (n2 - 2)2 (n2 - 4)).</td> 
            </tr> 
            <tr> 
              <td> 
                <a href="http://terminology.hl7.org/3.1.0/CodeSystem-v3-ProbabilityDistributionType.html#v3-ProbabilityDistri
                butionType-G">G</a> 
              </td> 
              <td> (gamma)</td> 
              <td> The gamma-distribution used for data that is skewed and bounded to the right, i.e. where
                 the maximum of the distribution curve is located near the origin. The g-distribution has
                 a two parameters a and b. The relationship to mean m and variance s2 is m = a b and s2
                 = a b2.</td> 
            </tr> 
            <tr> 
              <td> 
                <a href="http://terminology.hl7.org/3.1.0/CodeSystem-v3-ProbabilityDistributionType.html#v3-ProbabilityDistri
                butionType-LN">LN</a> 
              </td> 
              <td> log-normal</td> 
              <td> The logarithmic normal distribution is used to transform skewed random variable X into
                 a normally distributed random variable U = log X. The log-normal distribution can be specified
                 with the properties mean m and standard deviation s. Note however that mean m and standard
                 deviation s are the parameters of the raw value distribution, not the transformed parameters
                 of the lognormal distribution that are conventionally referred to by the same letters.
                 Those log-normal parameters mlog and slog relate to the mean m and standard deviation
                 s of the data value through slog2 = log (s2/m2 + 1) and mlog = log m - slog2/2.</td> 
            </tr> 
            <tr> 
              <td> 
                <a href="http://terminology.hl7.org/3.1.0/CodeSystem-v3-ProbabilityDistributionType.html#v3-ProbabilityDistri
                butionType-N">N</a> 
              </td> 
              <td> normal (Gaussian)</td> 
              <td> This is the well-known bell-shaped normal distribution. Because of the central limit theorem,
                 the normal distribution is the distribution of choice for an unbounded random variable
                 that is an outcome of a combination of many stochastic processes. Even for values bounded
                 on a single side (i.e. greater than 0) the normal distribution may be accurate enough
                 if the mean is &quot;far away&quot; from the bound of the scale measured in terms of standard
                 deviations.</td> 
            </tr> 
            <tr> 
              <td> 
                <a href="http://terminology.hl7.org/3.1.0/CodeSystem-v3-ProbabilityDistributionType.html#v3-ProbabilityDistri
                butionType-T">T</a> 
              </td> 
              <td> T</td> 
              <td> Used to describe the quotient of a normal random variable and the square root of a c2
                 random variable. The t-distribution has one parameter n, the number of degrees of freedom.
                 The relationship to mean m and variance s2 are: m = 0 and s2 = n / (n - 2)</td> 
            </tr> 
            <tr> 
              <td> 
                <a href="http://terminology.hl7.org/3.1.0/CodeSystem-v3-ProbabilityDistributionType.html#v3-ProbabilityDistri
                butionType-U">U</a> 
              </td> 
              <td> uniform</td> 
              <td> The uniform distribution assigns a constant probability over the entire interval of possible
                 outcomes, while all outcomes outside this interval are assumed to have zero probability.
                 The width of this interval is 2s sqrt(3). Thus, the uniform distribution assigns the probability
                 densities f(x) = sqrt(2 s sqrt(3)) to values m - s sqrt(3) &gt;= x &lt;= m + s sqrt(3)
                 and f(x) = 0 otherwise.</td> 
            </tr> 
            <tr> 
              <td> 
                <a href="http://terminology.hl7.org/3.1.0/CodeSystem-v3-ProbabilityDistributionType.html#v3-ProbabilityDistri
                butionType-X2">X2</a> 
              </td> 
              <td> chi square</td> 
              <td> Used to describe the sum of squares of random variables which occurs when a variance is
                 estimated (rather than presumed) from the sample. The only parameter of the c2-distribution
                 is n, so called the number of degrees of freedom (which is the number of independent parts
                 in the sum). The c2-distribution is a special type of g-distribution with parameter a
                 = n /2 and b = 2. Hence, m = n and s2 = 2 n.</td> 
            </tr> 
          </table> 
        </li> 
      </ul> 
    </div> 
  </text> 
  <extension url="http://hl7.org/fhir/StructureDefinition/structuredefinition-wg">
    <valueCode value="fhir"/> 
  </extension> 
  <url value="http://hl7.org/fhir/ValueSet/probability-distribution-type"/> 
  <identifier> 
    <system value="urn:ietf:rfc:3986"/> 
    <value value="urn:oid:2.16.840.1.113883.4.642.3.907"/> 
  </identifier> 
  <version value="5.0.0-ballot"/> 
  <name value="ProbabilityDistributionType"/> 
  <title value="ProbabilityDistributionType"/> 
  <status value="draft"/> 
  <experimental value="false"/> 
  <date value="2022-09-07T10:58:29+10:00"/> 
  <publisher value="HL7 (FHIR Project)"/> 
  <contact> 
    <telecom> 
      <system value="url"/> 
      <value value="http://hl7.org/fhir"/> 
    </telecom> 
    <telecom> 
      <system value="email"/> 
      <value value="fhir@lists.hl7.org"/> 
    </telecom> 
  </contact> 
  <description value="Codes specifying the type of probability distribution."/> 
  <compose> 
    <include> 
      <system value="http://terminology.hl7.org/CodeSystem/v3-ProbabilityDistributionType"/> 
      <concept> 
        <extension url="http://hl7.org/fhir/StructureDefinition/valueset-concept-definition">
          <valueString value="The beta-distribution is used for data that is bounded on both sides and might or might
           not be skewed (e.g., occurs when probabilities are estimated.) Two parameters a and b
           are available to adjust the curve. The mean m and variance s2 relate as follows: m = a/
           (a + b) and s2 = ab/((a + b)2 (a + b + 1))."/> 
        </extension> 
        <code value="B"/> 
        <display value="beta"/> 
      </concept> 
      <concept> 
        <extension url="http://hl7.org/fhir/StructureDefinition/valueset-concept-definition">
          <valueString value="Used for data that describes extinction. The exponential distribution is a special form
           of g-distribution where a = 1, hence, the relationship to mean m and variance s2 are m
           = b and s2 = b2."/> 
        </extension> 
        <code value="E"/> 
        <display value="exponential"/> 
      </concept> 
      <concept> 
        <extension url="http://hl7.org/fhir/StructureDefinition/valueset-concept-definition">
          <valueString value="Used to describe the quotient of two c2 random variables. The F-distribution has two parameters
           n1 and n2, which are the numbers of degrees of freedom of the numerator and denominator
           variable respectively. The relationship to mean m and variance s2 are: m = n2 / (n2 -
           2) and s2 = (2 n2 (n2 + n1 - 2)) / (n1 (n2 - 2)2 (n2 - 4))."/> 
        </extension> 
        <code value="F"/> 
        <display value="F"/> 
      </concept> 
      <concept> 
        <extension url="http://hl7.org/fhir/StructureDefinition/valueset-concept-definition">
          <valueString value="The gamma-distribution used for data that is skewed and bounded to the right, i.e. where
           the maximum of the distribution curve is located near the origin. The g-distribution has
           a two parameters a and b. The relationship to mean m and variance s2 is m = a b and s2
           = a b2."/> 
        </extension> 
        <code value="G"/> 
        <display value="(gamma)"/> 
      </concept> 
      <concept> 
        <extension url="http://hl7.org/fhir/StructureDefinition/valueset-concept-definition">
          <valueString value="The logarithmic normal distribution is used to transform skewed random variable X into
           a normally distributed random variable U = log X. The log-normal distribution can be specified
           with the properties mean m and standard deviation s. Note however that mean m and standard
           deviation s are the parameters of the raw value distribution, not the transformed parameters
           of the lognormal distribution that are conventionally referred to by the same letters.
           Those log-normal parameters mlog and slog relate to the mean m and standard deviation
           s of the data value through slog2 = log (s2/m2 + 1) and mlog = log m - slog2/2."/> 
        </extension> 
        <code value="LN"/> 
        <display value="log-normal"/> 
      </concept> 
      <concept> 
        <extension url="http://hl7.org/fhir/StructureDefinition/valueset-concept-definition">
          <valueString value="This is the well-known bell-shaped normal distribution. Because of the central limit theorem,
           the normal distribution is the distribution of choice for an unbounded random variable
           that is an outcome of a combination of many stochastic processes. Even for values bounded
           on a single side (i.e. greater than 0) the normal distribution may be accurate enough
           if the mean is &quot;far away&quot; from the bound of the scale measured in terms of standard
           deviations."/> 
        </extension> 
        <code value="N"/> 
        <display value="normal (Gaussian)"/> 
      </concept> 
      <concept> 
        <extension url="http://hl7.org/fhir/StructureDefinition/valueset-concept-definition">
          <valueString value="Used to describe the quotient of a normal random variable and the square root of a c2
           random variable. The t-distribution has one parameter n, the number of degrees of freedom.
           The relationship to mean m and variance s2 are: m = 0 and s2 = n / (n - 2)"/> 
        </extension> 
        <code value="T"/> 
        <display value="T"/> 
      </concept> 
      <concept> 
        <extension url="http://hl7.org/fhir/StructureDefinition/valueset-concept-definition">
          <valueString value="The uniform distribution assigns a constant probability over the entire interval of possible
           outcomes, while all outcomes outside this interval are assumed to have zero probability.
           The width of this interval is 2s sqrt(3). Thus, the uniform distribution assigns the probability
           densities f(x) = sqrt(2 s sqrt(3)) to values m - s sqrt(3) &gt;= x &lt;= m + s sqrt(3)
           and f(x) = 0 otherwise."/> 
        </extension> 
        <code value="U"/> 
        <display value="uniform"/> 
      </concept> 
      <concept> 
        <extension url="http://hl7.org/fhir/StructureDefinition/valueset-concept-definition">
          <valueString value="Used to describe the sum of squares of random variables which occurs when a variance is
           estimated (rather than presumed) from the sample. The only parameter of the c2-distribution
           is n, so called the number of degrees of freedom (which is the number of independent parts
           in the sum). The c2-distribution is a special type of g-distribution with parameter a
           = n /2 and b = 2. Hence, m = n and s2 = 2 n."/> 
        </extension> 
        <code value="X2"/> 
        <display value="chi square"/> 
      </concept> 
    </include> 
  </compose> 
</ValueSet>